Asymptotic Behavior and Subtractions in the Mandelstam Representation

It is proved that a two-body reaction amplitude involving scalar particles and satisfying Mandelstam's representation is bounded by expressions of the form $\mathrm{Cs}{\mathrm{ln}}^{2}s$ at the forward and backward angles, and $C{s}^{\frac{3}{4}}{\mathrm{ln}}^{\frac{3}{2}}s$ at any other fixed angle in the physical region, $C$ being a constant, $s$ being the total squared c.m. energy. This corresponds to cross sections increasing at most like ${\mathrm{ln}}^{2}s$. These restrictions limit the freedom of choice of the subtraction terms to six arbitrary single spectral functions and one subtraction constant.

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